There is one caveat: since the type of the generated structures
is different for each species, they must be cast (using the magic
of Data.Typeable) out of an existential wrapper; this is why
type annotations are required in all the examples above. Of
course, if a call to enumerate is used in the context of some
larger program, a type annotation will probably not be needed,
due to the magic of type inference.

For help in knowing what type annotation you can give when
enumerating the structures of a particular species at the ghci
prompt, see the structureType function. To be able to use your
own custom data type in an enumeration, just make your data type
an instance of the Enumerable type class; this can be done for
you automatically by Math.Combinatorics.Species.TH.

If an invalid type annotation is given, enumerate will call
error with a helpful error message. This should not be much of
an issue in practice, since usually enumerate will be used at a
specific type; it's hard to imagine a usage of enumerate which
will sometimes work and sometimes fail. However, those who like
their functions total can use extractStructure to make a
version of enumerate (or the other variants) with a return type
of [EitherString (f a)] (which will return an annoying ton of
duplicate error messages) or EitherString [f a] (which has the
unfortunate property of being much less lazy than the current
versions, since it must compute the entire list before deciding
whether to return Left or Right).

Labelled enumeration: given a species expression and a list of
labels (which are assumed to be distinct), compute the list of
all structures built from the given labels. If the type given
for the enumeration does not match the species expression (via an
Enumerable instance), call error with an error message
explaining the mismatch. This is slightly more efficient than
enumerate for lists of labels which are known to be distinct,
since it doesn't have to waste time checking for
duplicates. (However, it probably doesn't really make much
difference, since the time to do the actual enumeration will
usually dwarf the time to process the list of labels anyway.)

Unlabelled enumeration: given a species expression and an integer
indicating the number of labels to use, compute the list of all
unlabelled structures of the given size. If the type given for
the enumeration does not match the species expression, call
error with an error message explaining the mismatch.

General enumeration: given a species expression and a multiset of
labels, compute the list of all distinct structures built from
the given labels. If the type given for the enumeration does not
match the species expression, call error with a message
explaining the mismatch.

Tools for dealing with structure types

The Enumerable class allows you to enumerate structures of any
type, by declaring an instance of Enumerable. The Enumerable
instance requires you to declare a standard structure type (see
Math.Combinatorics.Species.Structures) associated with your
type, and a mapping iso from the standard type to your custom
one. Instances are provided for all the standard structure types
so you can enumerate species without having to provide your own
custom data type as the target of the enumeration if you don't
want to.

structureType s returns a String representation of the
functor type which represents the structure of the species s.
In particular, if structureType s prints "T", then you can
safely use enumerate and friends by writing

Note, however, that providing a type annotation on enumerate in
this way is usually only necessary at the ghci prompt; when used
in the context of a larger program the type of a call to
enumerate can often be inferred.

Show a TypeRep while stripping off qualifier portions of TyCon
names. This is essentially copied and pasted from the
Data.Typeable source, with a number of cases taken out that we
don't care about (special cases for (->), tuples, etc.).

Where all the work actually happens

Given an AST describing a species, with a phantom type parameter
representing the structure of the species, and an underlying
multiset of elements, compute a list of all possible structures
built over the underlying multiset. (Of course, it would be
really nice to have a real dependently-typed language for this!)

Unfortunately, TSpeciesAST cannot be made an instance of
Species, so if we want to be able to enumerate structures given
an expression of the Species DSL as input, the output must be
existentially quantified; see enumerateE.

Generating structures over base elements from a multiset
unifies labelled and unlabelled generation into one framework.
To enumerate labelled structures, use a multiset where each
element occurs exactly once; to enumerate unlabelled structures,
use a multiset with the desired number of copies of a single
element. To do labelled generation we could get away without the
generality of multisets, but to do unlabelled generation we need
the full generality anyway.

enumerate' does all the actual work, but is not meant to be used
directly; use one of the specialized enumerateXX methods.

enumerateE is a variant of enumerate' which takes an
(existentially quantified) typed AST and returns a list of
existentially quantified structures. This is also not meant to
be used directly. Instead, you should use one of the other
enumerateX methods.